The straight prism is based on a right-angled triangle with 6cm and 8cm legs. The side edge is equal to the largest

| August 4, 2021 | education

The straight prism is based on a right-angled triangle with 6cm and 8cm legs. The side edge is equal to the largest edge of the base. Find the surface area and volume of the prism.

Let us determine the length of the hypotenuse AB in the right-angled triangle ABC according to the Pythagorean theorem.

AB ^ 2 = AC ^ 2 + BC ^ 2 = 36 + 64 = 100.

AB = 10 cm.

By condition, the side edge is equal to the larger edge of the base, then AA1 = BB1 = CC1 = AB = 10 cm.

Determine the area of ​​the base.

Sosn = AC * BC / 2 = 6 * 8/2 = 24 cm.

Determine the perimeter of the base of the prism. Rosn = AB + BC + AC = 10 + 8 + 6 = 24 cm.

Let’s calculate the area of ​​the lateral surface of the prism. Sside = Rosn * AA1 = 24 * 10 = 240 cm2.

Then the total area is equal to: Sпов = Sbok + Sсн = 240 + 2 * 24 = 288 cm2.

Let’s define the volume of the prism.

V = Sbn * АА1 = 24 * 10 = 240 cm3.

Answer: The area of ​​the prism is 288 cm2, the volume is 240 cm3.



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